Bianchi type-III cosmological models with gravitational constant G and the cosmological constant Λ

Einstein field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-III universe by assuming conservation law for the energy-momentum tensor. Exact solutions of the field equations are obtained by using the scalar of expansion proportional to the shear scalar theta proportional to sigma, which leads to a relation between metric potential B = C-n, where n is a constant. The corresponding physical interpretation of the cosmological solutions are also discussed.